Direct evidence for a geometrically constrained "entatic state" effect on copper(II/I) electron-transfer kinetics as manifested in metastable intermediates

The absolute magnitude of an "entatic" (constrained) state effect has never been quantitatively demonstrated. In the current study, we have examined t he electron-transfer kinetics for five closely related copper(II/I) complex es formed with all possible diastereomers of [14]aneS(4) (1,4,X,11-tetrathi acyclotetradecane) in which both ethylene bridges have been replaced by cis - or trans-1,2-cyclohexane. The crystal structures of all five Cu(II) compl exes and a representative Cu(I) complex have been established by X-ray diff raction. For each complex. the cross-reaction rate constants have been dete rmined with six different oxidants and reductants in aqueous solution at 25 degreesC, mu = 0.10 M. The value of the electron self-exchange rate consta nt (k(11)) has then been calculated from each cross reaction rate constant using the Marcus cross relation. All five Cu(II/I) systems show evidence of a dual-pathway square scheme mechanism for which the two individual kit va lues have been evaluated. In combination with similar values previously det ermined for the parent complex, Cu-II/I([14]aneS(4)), and corresponding com plexes with the two related monocyclohexanediyl derivatives, we now have ev aluated a total of 16 self-exchange rate constants which span nearly 6 orde rs of magnitude for these 8 closely related Cu(II/I) systems. Application o f the stability constants for the formation of the corresponding 16 metasta ble intermediates-as previously determined by rapid-scan cyclic voltammetry -makes it possible to calculate the specific electron self-exchange rate co nstants representing the reaction of each of the strained intermediate spec ies exchanging electrons with their stable redox partners-the first time th at calculations of this type have been possible. All but three of these 16 specific self-exchange rate constants fall within-or very close to-the rang e of 10(5)-10(6) M-1 s(-1), values which are characteristic of the most lab ile Cu(II/I) systems previously reported, including the blue copper protein s. The results of the current investigation provide the first unequivocal d emonstration of the efficacy of the entatic state concept as applied to Cu( II/I) systems.